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The paper argues that a cheap bond-stretch benchmark can predict when machine-learned interatomic potentials will go unstable in molecular dynamics, and shows that using its metric to guide architecture design yields models that are both ac

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2026-08-03 04:23 UTC pith:GLAYBKE6

load-bearing objection Useful new benchmark and design-loop study for MLIP smoothness, but the 'correlates strongly with MD stability' claim is thinner than the abstract suggests. the 3 major comments →

arxiv 2602.04861 v2 pith:GLAYBKE6 submitted 2026-02-04 cs.LG cond-mat.mtrl-scics.AIphysics.chem-ph

From Evaluation to Design: Using Potential Energy Surface Smoothness Metrics to Guide Machine Learning Interatomic Potential Architectures

Ryan Liu , Eric Qu , Tobias Kreiman , Samuel M. Blau , Aditi S. Krishnapriyan This is my paper
classification cs.LG cond-mat.mtrl-scics.AIphysics.chem-ph
keywords bond smoothness characterization testforce smoothness deviationpotential energy surface smoothnessmachine learning interatomic potentialsmolecular dynamics stabilitydifferentiable k-nearest neighborsattention temperaturePES benchmark
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper is trying to establish that the smoothness of a machine-learned potential energy surface can be measured cheaply and that this measurement predicts simulation stability better than standard energy/force regression errors do. Its proposed test, BSCT, stretches and compresses individual bonds while holding the rest of each molecule frozen, then compares the MLIP's force curve to a DFT reference using a new metric, the Force Smoothness Deviation (FSD). The paper reports that FSD correlates strongly with kinetic-temperature spikes in high-temperature molecular dynamics while costing roughly 40 minutes versus 40 hours, and that using FSD as an in-the-loop design guide leads to concrete architectural choices—wider Gaussian smearing, temperature-controlled attention, and a differentiable k-nearest-neighbor graph—that together produce low regression error, stable MD, and robust property predictions. If this holds, BSCT/FSD gives MLIP developers a fast, physics-grounded screen for what current benchmarks miss, and turns evaluation itself into a design tool.

Core claim

The central discovery is that one-dimensional bond scans expose a failure mode of MLIPs that near-equilibrium test sets hide: artificial bumps and jumps in the predicted force as a bond is driven far from equilibrium. The paper defines FSD as the maximum over the scan of the difference in logarithmic derivatives of the force norm between the MLIP and DFT, a form chosen so that spurious extrema and inflection points are penalized in both low-force and high-force regions. Empirically, across three variants of an unconstrained Transformer-style testbed, higher FSD tracks more frequent and larger kinetic-temperature spikes in high-temperature simulation, providing evidence that FSD is a valid ea

What carries the argument

The paper's central object is the Force Smoothness Deviation (FSD), a scalar metric computed from BSCT's one-dimensional bond-scan curves; it is the maximum absolute difference between MLIP and DFT of d/dα log(||ΔF||_2) along the perturbation coordinate, and it is designed to flag artificial extrema and inflection points in the predicted potential energy surface. The supporting infrastructure is the BSCT dataset: 485 molecules scanned along bridge bonds with 100 DFT single points per molecule at frozen fragment geometries, filtered to exclude SCF discontinuities. Three architectural mechanisms carry the design story: a differentiable k-nearest-neighbor algorithm (Diff-kNN) that replaces hard

Load-bearing premise

The load-bearing premise, which the paper's final remarks partly concede, is that 1D frozen-fragment bond scans are representative of the far-from-equilibrium PES regions where MLIPs lose stability, and the reported FSD-MD correlation is demonstrated only across three variants of a single architecture family.

What would settle it

Run high-temperature MD on systems known to fail via torsional motion, collective rearrangements, or bond formation rather than simple bond stretching, and check whether FSD scores across models still rank MD stability correctly; a model with low FSD that still produces kinetic-temperature spikes would falsify the representativeness premise. A simpler, cheaper check: take a model with deliberately sharp smearing, low attention temperature, and standard nondifferentiable kNN so that 1D bond scans look smooth while regression error stays low, and see whether NVE energy drift or high-temperature

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • FSD on BSCT can replace expensive microcanonical MD as an early screening step: the paper reports a roughly 40-minute BSCT cost versus roughly 40-hour MD simulations for the same signal.
  • Model developers can use BSCT in the loop: the paper shows that targeted regularizations reduce FSD without sacrificing low energy/force regression error, so smoothness and accuracy are not in tension.
  • Larger models improve accuracy but degrade far-from-equilibrium smoothness, so scaling MLIPs without smoothness regularization is risky.
  • Nondifferentiable graph construction makes an MLIP non-conservative, producing large energy drift in NVE simulations, and the differentiable kNN algorithm restores energy conservation.
  • The BSCT-guided smoothness designs also improve near-equilibrium smoothness in the paper's materials-stability experiments, suggesting the design lessons transfer beyond molecules.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Beyond the paper: because BSCT probes only single-bond elongation with frozen fragments, instabilities driven by torsional rotations, collective multi-atom rearrangements, or bond formation could evade it; a natural extension is multi-coordinate and torsion scans and tests on such instabilities.
  • Beyond the paper: FSD's logarithmic-derivative form is not specific to bonds; it could be applied to any 1D slice of a PES (torsion profiles, reaction coordinates, lattice strains) as a general smoothness diagnostic.
  • Beyond the paper: the paper uses BSCT as an evaluation and design guide but not as a training objective; a testable extension is to use FSD or its gradients as a regularizer during training, which could smooth the PES directly rather than only at chosen scans.
  • Beyond the paper: the reported FSD-MD correlation is established within one architecture family; testing BSCT across diverse MLIP architectures would say whether FSD ranking is architecture-independent or only valid within a lineage.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. The paper introduces the Bond Smoothness Characterization Test (BSCT), a low-cost benchmark that probes a machine-learned interatomic potential (MLIP) along one-dimensional bond-stretch coordinates, and the Force Smoothness Deviation (FSD) metric, which measures how much the MLIP's force-norm profile deviates from the DFT reference. The authors claim that FSD correlates strongly with MD stability, and they use FSD as an in-the-loop design signal to iteratively modify a Transformer-based MLIP testbed (MinDScAIP), introducing Diff-kNN, wider Gaussian smearing, and temperature-controlled attention. The resulting model is reported to achieve low energy/force MAEs, stable MD, and competitive Matbench Discovery results. The BSCT-SPICE dataset and evaluation code are released publicly.

Significance. If the central correlation claim holds, BSCT/FSD is a valuable, cheap proxy for far-from-equilibrium PES smoothness and a useful design-time diagnostic. The metric is defined a priori from physical reasoning rather than fitted to MD outcomes, which mitigates circularity, and the public benchmark dataset is a concrete community resource. The architectural case study, especially Diff-kNN and attention-temperature regularization, addresses a real gap in conservative and smooth MLIP construction. However, the paper's headline claim that FSD 'correlates strongly with MD stability' is currently supported by only three variants of one architecture with no error bars and with a non-monotonic trend at 5000 K. The work is promising but needs substantially broader validation before the central claim is convincing.

major comments (3)
  1. [§5.2, Table 1] The central claim 'correlates strongly with MD stability' rests on exactly three MinDScAIP variants from one architecture. No error bars, confidence intervals, or correlation coefficients are reported. Moreover, the 5000 K column is non-monotonic: FSD values 97.4, 76.3, 43.2 correspond to max jumps 597, 509, 514 meV, so the lowest-FSD model does not have the lowest max jump. Please report per-trajectory distributions, a correlation statistic with uncertainty, and results across a broader set of architectures and models. The current evidence is too thin for the abstract's unqualified claim.
  2. [§3, Eq. (1) and Appendix A] BSCT samples only frozen-fragment, rigid bond-stretch displacements, and Appendix A step 6 explicitly excludes bonds whose DFT PES is discontinuous due to SCF convergence issues—exactly the bond-breaking regime most relevant for MLIP failures. MD instabilities can be triggered by collective rearrangements, torsional motion, or bond formation, none of which is sampled by a 1D bond stretch. The stress-test concern therefore lands: the 'strong correlation with MD stability' may not generalize to the actual failure modes in MD. Please demonstrate that the instabilities in the MD22 test systems occur along coordinates of the BSCT type (e.g., analyze spike geometries), or extend BSCT to torsional/collective probes.
  3. [§3, Eq. (3)] FSD is defined as the maximum over α of |d/dα log(‖ΔF_MLIP‖/‖ΔF_DFT‖)|. At the minimum-energy structure, both force norms vanish, so the logarithmic derivative is undefined. The paper does not specify a regularization floor, epsilon, or the numerical differentiation scheme used to evaluate the derivative. Since FSD is the paper's central measurable, this is a load-bearing technical gap. Please state the exact numerical procedure and check FSD sensitivity to the regularization.
minor comments (5)
  1. [Table 5] The text says 'Models are sorted in F1 order, with our model (MinDScAIP-60M) placed at the top,' but MatRIS-10M-MP has F1 0.847 versus MinDScAIP's 0.833. Either the table is not F1-sorted or the claim is inaccurate; please correct.
  2. [§4.2, Eq. (8)-(9)] The envelope function e=exp(-f^2/(1-f^2)) is undefined when f_env ≥ 1, but Eq. (9) can drive f_env above 1 when the distance cutoff term exceeds unity. Please specify the clipping or masking used in practice.
  3. [Appendix E] The sentence 'It is infinitely differentiable, and this also demonstrates that its higher derivatives are bounded' is logically invalid: infinite differentiability does not imply bounded derivatives on unbounded domains. The empirical NVE drift is the relevant evidence; please state the result as empirical rather than as a consequence of infinite differentiability.
  4. [Appendix D] The Gaussian-smearing derivative bound is derived by replacing a sum with an integral and then absorbing a(σz) into the maximization. This is heuristic; if the bound is used as a theoretical guarantee for the design choice, please provide a rigorous statement with error bounds or state the result as an approximate motivation.
  5. [General] Figure 6 and Table 1 would benefit from error bars or shaded regions over the 70 trajectories, and a statement about whether the differences are statistically significant. Also clarify the reported '~40 hours' for MD: is this the total cost for all trajectories or per trajectory?

Circularity Check

0 steps flagged

No definitional circularity: FSD is defined from physical reasoning and checked against independent MD stability; the in-the-loop design study is partly self-referential but does not reduce the central claim to its inputs.

full rationale

The FSD metric (Eqs. 3-4) is defined a priori as the maximum over a 1D bond-stretch coordinate of |d/dα log(||ΔF_MLIP||2 / ||ΔF_DFT||2)|. It contains no parameters fitted to MD outcomes and is computed against DFT references obtained independently at the SPICE level of theory. The claimed correlation with MD stability is therefore an empirical validation, not a tautology. The BSCT-guided design study is mildly self-referential: the proposed modifications (larger Gaussian smearing, higher attention temperature, weight decay) are regularizers that directly bound or smooth the derivatives that FSD measures, so improvements in FSD for those models are partly built into the design choices rather than independent predictions. However, the paper does not stop at FSD: it reports NVE energy drift (Appendix E) and high-temperature MD kinetic-temperature jumps (Table 1) as separate checks, and the final remarks explicitly caution that 'BSCT alone does not constitute a holistic evaluation.' The self-citations (e.g., Kreiman et al. on Transformer structure discovery, Qu & Krishnapriyan on kNN graphs) are contextual and are not the load-bearing support for the central metric-validity claim. The main caveats—three models from a single architecture, one non-monotonic 5000K row in Table 1, and Appendix A's exclusion of SCF-discontinuous bonds—are evidentiary weaknesses rather than circularity. Thus no significant circularity is found; a low score is appropriate.

Axiom & Free-Parameter Ledger

7 free parameters · 5 axioms · 0 invented entities

No new physical entity is postulated. The central objects are a benchmark probe and a scalar metric; their validity rests on the reference PES being smooth, on 1D scans being representative, and on hand-set hyperparameters for the architecture.

free parameters (7)
  • Gaussian smearing scale gamma (sigma = gamma * dx) = 1, 5, 10
    Chosen by hand to control radial-feature smoothness; larger values are claimed to upper-bound derivative magnitude.
  • Attention temperature tau = 1, 5, 10
    Introduced after inspecting BSCT attention spikes; larger values smooth attention outputs.
  • Weight decay strength = 1e-3, 1e-2, 5e-2
    Regularization strength; increased in smoothness-oriented variants.
  • Diff-kNN soft-rank scale d0 = 0.2 A
    Controls sigmoid sharpness in the soft ranking; hand-set hyperparameter.
  • Diff-kNN log-sum-exp beta = 10
    Controls softness of combining rank and distance envelopes; hand-set.
  • kNN degree k and radius cutoff r_c = k=30, r_c=6 A
    Graph construction hyperparameters chosen by hand.
  • BSCT scan range and sampling density = 0.5x-2x covalent radii, 100 points per bond
    Benchmark design choices determining which PES region is probed; not fitted to data but define the dataset.
axioms (5)
  • domain assumption Chemical smoothness means absence of artificial extrema, discontinuities, and inflection points
    Defines the target property and is cited to Subotnik et al. [53]; invoked throughout Section 3.
  • domain assumption DFT (omegaB97M-D3(BJ)/def2-TZVPPD) reference PES is smooth and accurate over the scanned bond lengths
    BSCT uses DFT as ground truth; SCF-inconsistent points are explicitly excluded in Appendix A.
  • domain assumption One-dimensional frozen-fragment bond scans capture the failure modes relevant to MD instability
    Eq. (1) displaces fragments only along the bond axis; collective, torsional, or multi-body instabilities may be missed.
  • domain assumption Kinetic-temperature jumps in high-temperature Langevin MD indicate PES non-smoothness
    Section 5.2 treats jumps much larger than the bath temperature within 10 fs as spurious-force events.
  • ad hoc to paper Infinitely differentiable potential has bounded higher derivatives
    Appendix E states this to explain why Diff-kNN conserves energy; it is false in general (e.g., exp(x^2)) and is load-bearing for the energy-conservation argument.

pith-pipeline@v1.3.0-alltime-deepseek · 20212 in / 11566 out tokens · 121125 ms · 2026-08-03T04:23:51.594565+00:00 · methodology

0 comments
read the original abstract

Machine Learning Interatomic Potentials (MLIPs) sometimes fail to reproduce the physical smoothness of the quantum potential energy surface (PES), leading to erroneous behavior in downstream simulations that standard energy and force regression evaluations can miss. Existing evaluations, such as microcanonical molecular dynamics (MD), are computationally expensive and primarily probe near-equilibrium states. To improve evaluation metrics for MLIPs, we introduce the Bond Smoothness Characterization Test (BSCT). This efficient benchmark probes the PES via controlled bond deformations and detects non-smoothness, including discontinuities, artificial minima, and spurious forces, both near and far from equilibrium. We show that BSCT correlates strongly with MD stability while requiring a fraction of the cost of MD. To demonstrate how BSCT can guide iterative model design, we utilize an unconstrained Transformer backbone as a testbed, illustrating how refinements such as a new differentiable $k$-nearest neighbors algorithm and temperature-controlled attention reduce artifacts identified by our metric. By optimizing model design systematically based on BSCT, the resulting MLIP simultaneously achieves a low conventional E/F regression error, stable MD simulations, and robust atomistic property predictions. Our results establish BSCT as both a validation metric for practitioners to assess MLIP utility and as an "in-the-loop" model design proxy that alerts MLIP developers to physical challenges that cannot be efficiently evaluated by current MLIP benchmarks. The BSCT dataset and evaluation are available on https://github.com/ryanliu30/bsct.git

Figures

Figures reproduced from arXiv: 2602.04861 by Aditi S. Krishnapriyan, Eric Qu, Ryan Liu, Samuel M. Blau, Tobias Kreiman.

Figure 1
Figure 1. Figure 1: Example of how the Bond Smoothness and Characterization Test (BSCT) is constructed. We show a [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: (a): Motivation for our proposed potential energy surface (PES) smoothness metric. We compare two [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: To study how different model design choices impact or improve PES smoothness, we design a neural [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: The Diff-kNN algorithm inherits the computational advantage of [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Example of how BSCT can serve as an in-the-loop evaluation for MLIP development. We probe a [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: We present empirical evidence of BSCT’s validity as a low-cost proxy to MD stability. We visualize [PITH_FULL_IMAGE:figures/full_fig_p010_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Challenges with using a k-Nearest-Neighbor graph construction. (a): Mean ( [PITH_FULL_IMAGE:figures/full_fig_p020_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: The energy drift of three different MinDScAIP models during microcanonical (NVE) ensembles averaged [PITH_FULL_IMAGE:figures/full_fig_p022_8.png] view at source ↗

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Reference graph

Works this paper leans on

69 extracted references · 12 linked inside Pith

  1. [1]

    P ., Simm, G., Ortner, C., and Csányi, G

    Batatia, I., Kovacs, D. P ., Simm, G., Ortner, C., and Csányi, G. Mace: Higher order equivariant message passing neural networks for fast and accurate force fields.Advances in neural information processing systems, 35:11423–11436, 2022. 13

    2022

  2. [2]

    P ., Kornbluth, M., Molinari, N., Smidt, T

    Batzner, S., Musaelian, A., Sun, L., Geiger, M., Mailoa, J. P ., Kornbluth, M., Molinari, N., Smidt, T. E., and Kozinsky, B. E (3)-equivariant graph neural networks for data-efficient and accurate interatomic potentials. Nature communications, 13(1):2453, 2022

    2022

  3. [3]

    and Parrinello, M

    Behler, J. and Parrinello, M. Generalized neural-network representation of high-dimensional potential-energy surfaces.Physical review letters, 98(14):146401, 2007

    2007

  4. [4]

    The dark side of the forces: assessing non-conservative force models for atomistic machine learning, 2024

    Bigi, F., Langer, M., and Ceriotti, M. The dark side of the forces: assessing non-conservative force models for atomistic machine learning, 2024

    2024

  5. [5]

    Graph atomic cluster expansion for semilocal interactions beyond equivariant message passing.Physical Review X, 14(2):021036, 2024

    Bochkarev, A., Lysogorskiy, Y ., and Drautz, R. Graph atomic cluster expansion for semilocal interactions beyond equivariant message passing.Physical Review X, 14(2):021036, 2024

    2024

  6. [6]

    Open catalyst 2020 (oc20) dataset and community challenges.Acs Catalysis, 11(10): 6059–6072, 2021

    Chanussot, L., Das, A., Goyal, S., Lavril, T., Shuaibi, M., Riviere, M., Tran, K., Heras-Domingo, J., Ho, C., Hu, W., et al. Open catalyst 2020 (oc20) dataset and community challenges.Acs Catalysis, 11(10): 6059–6072, 2021

    2020

  7. [7]

    and Ong, S

    Chen, C. and Ong, S. P . A universal graph deep learning interatomic potential for the periodic table.Nature Computational Science, 2(11):718–728, 2022

    2022

  8. [8]

    Cartesian atomic cluster expansion for machine learning interatomic potentials, 2024

    Cheng, B. Cartesian atomic cluster expansion for machine learning interatomic potentials, 2024. URL https://arxiv.org/abs/2402.07472

    Pith/arXiv arXiv 2024

  9. [9]

    C., Weaver, E

    Chiang, Y ., Kreiman, T., Zhang, C., Kuner, M. C., Weaver, E. J., Amin, I., Park, H., Lim, Y ., Kim, J., Chrzan, D., Walsh, A., Blau, S. M., Asta, M., and Krishnapriyan, A. S. MLIP arena: Advancing fairness and transparency in machine learning interatomic potentials via an open, accessible benchmark platform. InThe Thirty-ninth Annual Conference on Neural...

    2025

  10. [10]

    T., Kabylda, A., Sauceda, H

    Chmiela, S., V assilev-Galindo, V ., Unke, O. T., Kabylda, A., Sauceda, H. E., Tkatchenko, A., and Müller, K.-R. Accurate global machine learning force fields for molecules with hundreds of atoms.Science Advances, 9(2):eadf0873, 2023

    2023

  11. [11]

    F., Gupta, V ., Romero, A

    Choudhary, K., Wines, D., Li, K., Garrity, K. F., Gupta, V ., Romero, A. H., Krogel, J. T., Saritas, K., Fuhr, A., Ganesh, P ., et al. Jarvis-leaderboard: a large scale benchmark of materials design methods.npj Computational Materials, 10(1):93, 2024

    2024

  12. [12]

    Cole, D. J. and Hine, N. D. Applications of large-scale density functional theory in biology.Journal of Physics: Condensed Matter, 28(39):393001, 2016

    2016

  13. [13]

    J., and Ceder, G

    Deng, B., Zhong, P ., Jun, K., Riebesell, J., Han, K., Bartel, C. J., and Ceder, G. Chgnet as a pretrained universal neural network potential for charge-informed atomistic modelling.Nature Machine Intelligence, 5(9):1031–1041, 2023

    2023

  14. [14]

    K., Dotson, D

    Eastman, P ., Behara, P . K., Dotson, D. L., Galvelis, R., Herr, J. E., Horton, J. T., Mao, Y ., Chodera, J. D., Pritchard, B. P ., Wang, Y ., et al. Spice, a dataset of drug-like molecules and peptides for training machine learning potentials.Scientific Data, 10(1):11, 2023

    2023

  15. [15]

    Forces are not enough: Benchmark and critical evaluation for machine learning force fields with molecular simulations.arXiv preprint arXiv:2210.07237, 2022

    Fu, X., Wu, Z., Wang, W., Xie, T., Keten, S., Gomez-Bombarelli, R., and Jaakkola, T. Forces are not enough: Benchmark and critical evaluation for machine learning force fields with molecular simulations.arXiv preprint arXiv:2210.07237, 2022. 14

    Pith/arXiv arXiv 2022

  16. [16]

    M., Barroso-Luque, L., Levine, D

    Fu, X., Wood, B. M., Barroso-Luque, L., Levine, D. S., Gao, M., Dzamba, M., and Zitnick, C. L. Learning smooth and expressive interatomic potentials for physical property prediction.arXiv preprint arXiv:2502.12147, 2025

    Pith/arXiv arXiv 2025

  17. [17]

    Directional message passing for molecular graphs.arXiv preprint arXiv:2003.03123, 2020

    Gasteiger, J., Groß, J., and Günnemann, S. Directional message passing for molecular graphs.arXiv preprint arXiv:2003.03123, 2020

    Pith/arXiv arXiv 2003

  18. [18]

    Gemnet: Universal directional graph neural networks for molecules.Advances in Neural Information Processing Systems, 34:6790–6802, 2021

    Gasteiger, J., Becker, F., and Günnemann, S. Gemnet: Universal directional graph neural networks for molecules.Advances in Neural Information Processing Systems, 34:6790–6802, 2021

    2021

  19. [19]

    J., Heidar-Zadeh, F., Liu, M., Head-Gordon, M., Bertels, L., et al

    Haghighatlari, M., Li, J., Guan, X., Zhang, O., Das, A., Stein, C. J., Heidar-Zadeh, F., Liu, M., Head-Gordon, M., Bertels, L., et al. Newtonnet: a newtonian message passing network for deep learning of interatomic potentials and forces.Digital Discovery, 1(3):333–343, 2022

    2022

  20. [20]

    Geometric numerical integration illustrated by the störmer–verlet method.Acta numerica, 12:399–450, 2003

    Hairer, E., Lubich, C., and Wanner, G. Geometric numerical integration illustrated by the störmer–verlet method.Acta numerica, 12:399–450, 2003

    2003

  21. [21]

    and Nørskov, J

    Hammer, B. and Nørskov, J. K. Theoretical surface science and catalysis—calculations and concepts. In Advances in catalysis, volume 45, pp. 71–129. Elsevier, 2000

    2000

  22. [22]

    and Rappoport, D

    Hellweg, A. and Rappoport, D. Development of new auxiliary basis functions of the karlsruhe segmented contracted basis sets including diffuse basis functions (def2-svpd, def2-tzvppd, and def2-qvppd) for ri-mp2 and ri-cc calculations.Physical Chemistry Chemical Physics, 17(2):1010–1017, 2015

    2015

  23. [23]

    Jain, A., Shin, Y ., and Persson, K. A. Computational predictions of energy materials using density functional theory.Nature Reviews Materials, 1(1):1–13, 2016

    2016

  24. [24]

    T., Suárez-Dou, S., Khabibrakhmanov, A., Medrano Sandonas, L., Unke, O

    Kabylda, A., Frank, J. T., Suárez-Dou, S., Khabibrakhmanov, A., Medrano Sandonas, L., Unke, O. T., Chmiela, S., Müller, K.-R., and Tkatchenko, A. Molecular simulations with a pretrained neural network and universal pairwise force fields.Journal of the American Chemical Society, 147(37):33723–33734, 2025

    2025

  25. [25]

    and Sham, L

    Kohn, W. and Sham, L. J. Self-consistent equations including exchange and correlation effects.Physical review, 140(4A):A1133, 1965

    1965

  26. [26]

    P ., Moore, J

    Kovács, D. P ., Moore, J. H., Browning, N. J., Batatia, I., Horton, J. T., Kapil, V ., Witt, W. C., Magd˘au, I.-B., Cole, D. J., and Csányi, G. Mace-off23: Transferable machine learning force fields for organic molecules. arXiv preprint arXiv:2312.15211, 2023

    Pith/arXiv arXiv 2023

  27. [27]

    and Krishnapriyan, A

    Kreiman, T. and Krishnapriyan, A. S. Understanding and mitigating distribution shifts for universal machine learning interatomic potentials.Digital Discovery, 2026

    2026

  28. [28]

    Kreiman, T., Bai, Y ., Atieh, F., Weaver, E., Qu, E., and Krishnapriyan, A. S. Transformers discover molecular structure without graph priors.arXiv preprint arXiv:2510.02259, 2025

    arXiv 2025

  29. [29]

    H., Mortensen, J

    Larsen, A. H., Mortensen, J. J., Blomqvist, J., Castelli, I. E., Christensen, R., Dułak, M., Friis, J., Groves, M. N., Hammer, B., Hargus, C., Hermes, E. D., Jennings, P . C., Jensen, P . B., Kermode, J., Kitchin, J. R., Kolsbjerg, E. L., Kubal, J., Kaasbjerg, K., Lysgaard, S., Maronsson, J. B., Maxson, T., Olsen, T., Pastewka, L., Peterson, A., Rostgaard...

    2017

  30. [30]

    S., Liesen, N., Chua, L., Diffenderfer, J., Ingolfsson, H., Kroonblawd, M

    Levine, D. S., Liesen, N., Chua, L., Diffenderfer, J., Ingolfsson, H., Kroonblawd, M. P ., Kumar, N., Maiti, A., Mohottalalage, S. S., Shuaibi, M., Essen, B. V ., Wood, B. M., Zitnick, C. L., Blau, S. M., and Antoniuk, E. R. The open polymers 2026 (opoly26) dataset and evaluations, 2025. URL https://arxiv.org/abs/2512.23117

    arXiv 2026

  31. [31]

    S., Shuaibi, M., Spotte-Smith, E

    Levine, D. S., Shuaibi, M., Spotte-Smith, E. W. C., Taylor, M. G., Hasyim, M. R., Michel, K., Batatia, I., Csányi, G., Dzamba, M., Eastman, P ., et al. The open molecules 2025 (omol25) dataset, evaluations, and models.arXiv preprint arXiv:2505.08762, 2025

    arXiv 2025

  32. [32]

    Equiformerv2: Improved equivariant transformer for scaling to higher-degree representations.arXiv preprint arXiv:2306.12059, 2023

    Liao, Y .-L., Wood, B., Das, A., and Smidt, T. Equiformerv2: Improved equivariant transformer for scaling to higher-degree representations.arXiv preprint arXiv:2306.12059, 2023

    Pith/arXiv arXiv 2023

  33. [33]

    Generalizing denoising to non-equilibrium structures improves equivariant force fields.arXiv preprint arXiv:2403.09549, 2024

    Liao, Y .-L., Smidt, T., Shuaibi, M., and Das, A. Generalizing denoising to non-equilibrium structures improves equivariant force fields.arXiv preprint arXiv:2403.09549, 2024

    Pith/arXiv arXiv 2024

  34. [34]

    Swin transformer: Hierarchical vision transformer using shifted windows

    Liu, Z., Lin, Y ., Cao, Y ., Hu, H., Wei, Y ., Zhang, Z., Lin, S., and Guo, B. Swin transformer: Hierarchical vision transformer using shifted windows. InProceedings of the IEEE/CVF international conference on computer vision, pp. 10012–10022, 2021

    2021

  35. [35]

    Mardirossian, N. and Head-Gordon, M.ωb97m-v: A combinatorially optimized, range-separated hybrid, meta-gga density functional with vv10 nonlocal correlation.The Journal of chemical physics, 144(21), 2016

    2016

  36. [36]

    Pet-mad, a lightweight universal interatomic potential for advanced materials modeling, 2025

    Mazitov, A., Bigi, F., Kellner, M., Pegolo, P ., Tisi, D., Fraux, G., Pozdnyakov, S., Loche, P ., and Ceriotti, M. Pet-mad, a lightweight universal interatomic potential for advanced materials modeling, 2025. URL https://arxiv.org/abs/2503.14118

    Pith/arXiv arXiv 2025

  37. [37]

    Miret, S., Lee, K. L. K., Gonzales, C., Mannan, S., and Krishnan, N. Energy & force regression on dft trajectories is not enough for universal machine learning interatomic potentials, 2025

    2025

  38. [38]

    J., Kornbluth, M., and Kozinsky, B

    Musaelian, A., Batzner, S., Johansson, A., Sun, L., Owen, C. J., Kornbluth, M., and Kozinsky, B. Learning local equivariant representations for large-scale atomistic dynamics.Nature Communications, 14(1):579, 2023

    2023

  39. [39]

    Orb: A fast, scalable neural network potential (2024), 2024

    Neumann, M., Gin, J., Rhodes, B., Bennett, S., Li, Z., Choubisa, H., Hussey, A., and Godwin, J. Orb: A fast, scalable neural network potential (2024), 2024

    2024

  40. [40]

    Scalable parallel algorithm for graph neural network interatomic potentials in molecular dynamics simulations.Journal of chemical theory and computation, 20(11): 4857–4868, 2024

    Park, Y ., Kim, J., Hwang, S., and Han, S. Scalable parallel algorithm for graph neural network interatomic potentials in molecular dynamics simulations.Journal of chemical theory and computation, 20(11): 4857–4868, 2024

    2024

  41. [41]

    P ., Simeon, G., Galvelis, R., Mirarchi, A., Eastman, P ., Doerr, S., Tholke, P ., Markland, T

    Pelaez, R. P ., Simeon, G., Galvelis, R., Mirarchi, A., Eastman, P ., Doerr, S., Tholke, P ., Markland, T. E., and De Fabritiis, G. Torchmd-net 2.0: Fast neural network potentials for molecular simulations, 2024

    2024

  42. [42]

    Thermal conductivity predictions with foundation atomistic models.arXiv preprint arXiv:2408.00755, 2024

    Póta, B., Ahlawat, P ., Csányi, G., and Simoncelli, M. Thermal conductivity predictions with foundation atomistic models.arXiv preprint arXiv:2408.00755, 2024

    Pith/arXiv arXiv 2024

  43. [43]

    and Ceriotti, M

    Pozdnyakov, S. and Ceriotti, M. Smooth, exact rotational symmetrization for deep learning on point clouds. Advances in Neural Information Processing Systems, 36:79469–79501, 2023

    2023

  44. [44]

    and Krishnapriyan, A

    Qu, E. and Krishnapriyan, A. The importance of being scalable: Improving the speed and accuracy of neural network interatomic potentials across chemical domains.Advances in Neural Information Processing Systems, 37:139030–139053, 2024. 16

    2024

  45. [45]

    K., Sresht, V ., Y ang, Q., Unwalla, R., Tu, M., Mathiowetz, A

    Rai, B. K., Sresht, V ., Y ang, Q., Unwalla, R., Tu, M., Mathiowetz, A. M., and Bakken, G. A. Torsionnet: A deep neural network to rapidly predict small-molecule torsional energy profiles with the accuracy of quantum mechanics.Journal of Chemical Information and Modeling, 62(4):785–800, 2022

    2022

  46. [46]

    Raja, S., Amin, I., Pedregosa, F., and Krishnapriyan, A. S. Stability-aware training of machine learning force fields with differentiable boltzmann estimators.Transactions on Machine Learning Research, 2025. ISSN 2835-8856. URLhttps://openreview.net/forum?id=ZckLMG00sO

    2025

  47. [47]

    and Furche, F

    Rappoport, D. and Furche, F. Property-optimized gaussian basis sets for molecular response calculations. The Journal of chemical physics, 133(13), 2010

    2010

  48. [48]

    Orb-v3: atomistic simulation at scale, 2025

    Rhodes, B., V andenhaute, S., Šimkus, V ., Gin, J., Godwin, J., Duignan, T., and Neumann, M. Orb-v3: atomistic simulation at scale, 2025

    2025

  49. [49]

    E., Benner, P ., Chiang, Y ., Deng, B., Lee, A

    Riebesell, J., Goodall, R. E., Benner, P ., Chiang, Y ., Deng, B., Lee, A. A., Jain, A., and Persson, K. A. Matbench discovery–a framework to evaluate machine learning crystal stability predictions.arXiv preprint arXiv:2308.14920, 2023

    Pith/arXiv arXiv 2023

  50. [50]

    Rowan Benchmarks, 2025

    Rowan Scientific Corporation. Rowan Benchmarks, 2025. URLhttps://benchmarks.rowansci. com/. Accessed: 2025-05-08

    2025

  51. [51]

    T., Sauceda, H

    Schütt, K. T., Sauceda, H. E., Kindermans, P .-J., Tkatchenko, A., and Müller, K.-R. Schnet–a deep learning architecture for molecules and materials.The Journal of Chemical Physics, 148(24), 2018

    2018

  52. [52]

    S., Isayev, O., and Roitberg, A

    Smith, J. S., Isayev, O., and Roitberg, A. E. Ani-1: an extensible neural network potential with dft accuracy at force field computational cost.Chemical science, 8(4):3192–3203, 2017

    2017

  53. [53]

    E., Sodt, A., and Head-Gordon, M

    Subotnik, J. E., Sodt, A., and Head-Gordon, M. The limits of local correlation theory: Electronic delocalization and chemically smooth potential energy surfaces.The Journal of chemical physics, 128(3), 2008

    2008

  54. [54]

    Team, F. C. Open molecules 2025 leaderboard. https://github.com/facebookresearch/ fairchem, 2024

    2025

  55. [55]

    M., Simmonett, A

    Turney, J. M., Simmonett, A. C., Parrish, R. M., Hohenstein, E. G., Evangelista, F. A., Fermann, J. T., Mintz, B. J., Burns, L. A., Wilke, J. J., Abrams, M. L., et al. Psi4: an open-source ab initio electronic structure program.Wiley Interdisciplinary Reviews: Computational Molecular Science, 2(4):556–565, 2012

    2012

  56. [56]

    M., Dzamba, M., Fu, X., Gao, M., Shuaibi, M., Barroso-Luque, L., Abdelmaqsoud, K., Gharakhanyan, V ., Kitchin, J

    Wood, B. M., Dzamba, M., Fu, X., Gao, M., Shuaibi, M., Barroso-Luque, L., Abdelmaqsoud, K., Gharakhanyan, V ., Kitchin, J. R., Levine, D. S., Michel, K., Sriram, A., Cohen, T., Das, A., Rizvi, A., Sahoo, S. J., Ulissi, Z. W., and Zitnick, C. L. Uma: A family of universal models for atoms, 2025. URL https://arxiv.org/abs/2506.23971

    arXiv 2025

  57. [57]

    A materials foundation model via hybrid invariant-equivariant architectures,

    Y an, K., Bohde, M., Kryvenko, A., Xiang, Z., Zhao, K., Zhu, S., Kolachina, S., Sarıtürk, D., Xie, J., Arroyave, R., Qian, X., Qian, X., and Ji, S. A materials foundation model via hybrid invariant-equivariant architectures,

  58. [58]

    C.-Y ., Kumar, A., Guan, X., Hermes, E

    Y uan, E. C.-Y ., Kumar, A., Guan, X., Hermes, E. D., Rosen, A. S., Zádor, J., Head-Gordon, T., and Blau, S. M. Analytical ab initio hessian from a deep learning potential for transition state optimization.Nature Communications, 15(1):8865, 2024. 17

    2024

  59. [59]

    C.-Y ., Liu, Y ., Chen, J., Zhong, P ., Raja, S., Kreiman, T., V argas, S., Xu, W., Head-Gordon, M., Y ang, C., et al

    Y uan, E. C.-Y ., Liu, Y ., Chen, J., Zhong, P ., Raja, S., Kreiman, T., V argas, S., Xu, W., Head-Gordon, M., Y ang, C., et al. Foundation models for atomistic simulation of chemistry and materials.arXiv preprint arXiv:2503.10538, 2025

    Pith/arXiv arXiv 2025

  60. [60]

    Deepmd-kit v2: A software package for deep potential models.The Journal of Chemical Physics, 159(5), 2023

    Zeng, J., Zhang, D., Lu, D., Mo, P ., Li, Z., Chen, Y ., Rynik, M., Huang, L., Li, Z., Shi, S., et al. Deepmd-kit v2: A software package for deep potential models.The Journal of Chemical Physics, 159(5), 2023

    2023

  61. [61]

    A graph neural network for the era of large atomistic models, 2026

    Zhang, D., Peng, A., Cai, C., Li, W., Zhou, Y ., Zeng, J., Guo, M., Zhang, C., Li, B., Jiang, H., Zhu, T., Jia, W., Zhang, L., and Wang, H. A graph neural network for the era of large atomistic models, 2026. URL https://arxiv.org/abs/2506.01686

    arXiv 2026

  62. [62]

    S., Leszczynski, J., and Isayev, O

    Zubatyuk, R., Smith, J. S., Leszczynski, J., and Isayev, O. Accurate and transferable multitask prediction of chemical properties with an atoms-in-molecules neural network.Science advances, 5(8):eaav6490, 2019. 18 A BSCT Sampling Procedure The BSCT-SPICE dataset is constructed with the following procedure

    2019

  63. [64]

    Identify all candidate bridge bonds that partition the molecule into two separate fragments without creating isolated atoms

  64. [65]

    Linearly stretch and compress candidate bonds, covering bond lengths from0.5× to 2× the sum of the bonded atoms’ covalent radii

  65. [66]

    Exclude candidate bonds if, upon perturbation, any pair of atoms (except the pair bonded by the candidate) becomes closer than0.9×the sum of the bonded atoms’ covalent radii

  66. [67]

    Sample from the filtered dataset across selected bond types (C–C, C–N, C–O, C–P , C–S, N–N, N–O, N–P , and O–P)

  67. [68]

    Run DFT on 100 evenly spaced structures along each selected bond perturbation trajectory

  68. [69]

    smoothness

    Exclude bonds with discontinuous PES due to Self-Consistent Field convergence issues. Since the sampling process is random, we counteracted the arbitrariness by controlling the bond types that we sample, such as C-C, C-O, etc., since bond types are the most indicative property of a bond. We also set the bond lengths of the bridge bond independently by the...

  69. [2025]

    URLhttps://arxiv.org/abs/2503.05771

    Pith/arXiv arXiv